| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
|
| Initial Amendment Date: | August 24, 2011 |
| Latest Amendment Date: | August 24, 2011 |
| Award Number: | 1108780 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Victor Roytburd
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2011 |
| End Date: | August 31, 2015 (Estimated) |
| Total Intended Award Amount: | $148,899.00 |
| Total Awarded Amount to Date: | $148,899.00 |
| Funds Obligated to Date: |
|
| History of Investigator: |
|
| Recipient Sponsored Research Office: |
2800 VICTORY BLVD STATEN ISLAND NY US 10314-6609 (718)982-2254 |
| Sponsor Congressional District: |
|
| Primary Place of Performance: |
2800 VICTORY BLVD STATEN ISLAND NY US 10314-6609 |
| Primary Place of
Performance Congressional District: |
|
| Unique Entity Identifier (UEI): |
|
| Parent UEI: |
|
| NSF Program(s): | APPLIED MATHEMATICS |
| Primary Program Source: |
|
| Program Reference Code(s): |
|
| Program Element Code(s): |
|
| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
The objective of this collaborative research project is to develop methods for analysis, modeling, and computation for stochastic partial differential equations arising in nonlinear optics. The study of noise in these systems is complicated by several factors. In particular:
(i) the complexity due to the interplay of many physical effects,
(ii) the presence of multiple length and time scales, and
(iii) the fact that the critical events that represent system failures are, by design, extremely rare. We will address these challenges by (a) creating a set of analytical methods to obtain reductions from the stochastic partial differential equations that govern the system's behavior to a set of low-dimensional stochastic differential equations;
(b) developing efficient methods for the study of noise across multiple time and space scales; and (c) implementing hybrid analytical-computational methods that can efficiently target the rare events of interest and ultimately estimate the reliability of these systems.
Lightwave systems have a wide range of applications, in particular as lasers and optical communication lines, and their emergence has had a dramatic impact on our lives over the last fifty years. Lasers are used at low powers in applications related to scanning and communications; at higher powers they are employed in surgical and industrial applications. As noise is a major limiting factor in optical systems, further technological progress will depend critically on understanding the impact of noise and on being able to control noise-induced system failures. This research will provide new analytical and computational tools that support the analysis and design of the next generation of optical devices.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
Note:
When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external
site maintained by the publisher. Some full text articles may not yet be available without a
charge during the embargo (administrative interval).
Some links on this page may take you to non-federal websites. Their policies may differ from
this site.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Over the last decades, technology based on optical devices has dramatically changed our lives: One example are optical networks which allow us to communicate and exchange information, a second example are laser-based technologies ranging from optical atomic clocks to medical applications like surgery.
In a great deal of such devices, random fluctuations impact their performance and can potentially lead to failure or outage. In the context of optical communications, this is for example a 'bit error', when a pulse corresponding to a 'one' gets distorted to a 'zero' (or a 'zero' is, due to fluctuations, interpreted as a 'one'). A detailed understanding of such failure probabilities, caused by rare but important events, is essential for successful operation of such devices. However, since the events are rare and the systems are complex, the probability of such extreme events is difficult to compute.
In this project, we developed efficient algorithms to compute the likelihood of rare events based on a combination of numerical and analytical techniques based on so-called "instantons", which are particular mathematical objects that can be used to characterize the tails of the underlying probability distributions. Our algorithms to compute instantons were implemented and tested using particular examples. They are portable and can be applied to many model equations beyond nonlinear optics, in particular to fluid equations or biological systems.
The project involved the training of PhD students.
Last Modified: 11/28/2015
Modified by: Tobias B Schaefer
Please report errors in award information by writing to: awardsearch@nsf.gov.
